Why is it that we see light the way we do? Or, rephrased slightly, would we expect creatures from other worlds to see the same way we do?
The answer to the first question is part biological, part chemical and part astronomical. The short version is a combination of the convenient chemistry of the molecules already in living cells plus the energy of light plus a whole lot of light from the sun plus evolution equals an affinity in earth-bound creatures towards the narrow band of visible light.
Black body Radiators
Our local star can be thought of, save for a couple exceptions, as a black-body radiator. What this means is (nearly) all the light comes from the sun itself (as opposed to being reflected off something) and the color and intensity of the light is determined primarily by the temperature of the sun.
Black body radiators emit light of all wavelengths up to some cutoff point. They have a peak wavelength—that is, the wavelength of light they emit the strongest—a little below the cutoff. Both the cutoff point and peak are determined by the object’s temperature. As you increase the temperature, the peak (and the cutoff) move towards shorter wavelengths while at the same time the amount of light (brightness) increases across all wavelengths.
What does this have to do with how we see? The human eye is well tuned—not coincidentally—to the peak of a black body radiator the same temperature as the sun, or about 550 nm. Serious nerds will immediately recognize 550 nm as green light. Most people don’t see everything as having a green hue, so what do I mean by tuning? Basically our color perception is centered around green. We can see a little lower (red) and a little higher (blue) and our brain interprets anything in between. Also, our night vision—which is monochromatic—is most sensitive to green light. A weak green light at night should be just barely visible, while any other color of the same brightness will to too faint to see.
It is reasonable to speculate that creatures from other planets, assuming they have some sensory organ that reacts to light, would have similar tunings to their respective parent stars. Using this speculation we would think aliens from dim, red stars would have excellent low light vision that is more sensitive to near-infrared than us. Perhaps they are missing any sensitivity above say, what we call green light. Stop lights on earth would appear to only light up red and yellow, the green being out of their range of perception! On the other hand, something from a hot, blue star might be unusually sensitive to ultraviolet light, and not too sensitive at all to red.
While the star might be different in every alien world, chemistry and physics are the same everywhere. There is likely some limit to what biological creatures could “see” regardless of where they evolved. The reason you aren’t likely to find a creature with radio eyes is that radio is so low in energy it doesn’t really interact much with matter. Visible light on the other hand is relatively energetic and very good at affecting chemistry. There is a side problem of resolution too, the longer the wavelength of light (the more red) the bigger a detector (eye) you need to get the same resolution. Infrared-vision aliens would have to have have pretty huge eyes to match the visual acuity of humans.
Going to other direction brings up other problems. The shorter the wavelength of light (bluer) the more energetic it is, until around UV it starts stripping electrons off of atoms, actually destroying structures meant to detect it. This does not rule out x-ray vision, but it does make it a little harder to believe.
One last thing of note, colors as we see them are based around the unchanging physical properties of light, but their interpretation is entirely up to the brain! There is no reason that what we call orange looks the same to say, a bird, even though the light is the same in both cases. There is near infinite room for imagination to how aliens might perceive whatever kind of light they can detect. For instance they might be color blind, but wildly sensitive to a huge range of light, if they are from a binary star system. I can imagine them being able to both see the (invisible to us) IR lights on tv-remotes blinking as we change channels and the subtle patterns on flower petals visible only in UV. Or perhaps a species that can use its whole body as a thermal-IR detector. They would make fantastic repairmen, being able to see hot spots in electrical equipment or poorly greased bearings.
There are many reasons to make interactions between aliens and humans (or other aliens) complicated. Conflict is a key to plot. So why not add some complications around vision? One of both parties could be quite confused about why the other can’t see things they way they do, literally and figuratively.